Too Many Doctors, by Holly Roth (epub/Kindle/pdf)

The first victim is an attractive young woman who falls down stairs-or was she pushed?-and is then attacked next day with a razor blade. Luckily for somebody, she is suffering from amnesia as a result of the fall. Almost immediately thereafter another woman, who has been boasting about the acuteness of her senses, is thrown into the empty swimming pool, and is quite evidently lying about who did it.

Meanwhile, a doctor in London is murdered, and the police fish a body out of the Thames, also murdered, also a doctor. Back on the ship, an investigation discloses the fact that the ship's former doctor had died at sea before reaching Southampton-seemingly from a bout of indigestion, but actually from poison.

These are not unrelated events. How they are tied together makes for a constantly exciting, baffling, and suspenseful novel by a 20th Century master of the mystery genre!